Area of a Triangle

Class 6 Maths · Chapter 6: Perimeter and Area · NCERT Ganita Prakash section 6.3

Learn

Draw a rectangle 6 cm by 4 cm. Its area is 6 × 4 = 24 sq cm.

Cut it along a diagonal (corner to corner). We get two triangles that fit exactly on each other, so each one is half the rectangle.

24 ÷ 2 = 12 sq cm

What if the top point is somewhere else? Draw the height straight down. Each coral piece A outside matches a blue piece A inside, and the same for B. So the triangle is still half the rectangle!

So for any triangle: area = ½ × base × height. The height is the straight-up distance from the base to the top point.

½ × 8 × 5 = 20 sq cm

Try it! Move the top point left and right. The triangle changes shape, but its area stays the same, because base and height do not change.

Making it more or less: 8 unit squares can make shapes with different perimeters. A 4 × 2 rectangle has perimeter 12 units; a long line of 8 has perimeter 18 units. Same area, different perimeter!

Count only the outside edges. When two squares touch, that edge is inside the shape and is not part of the perimeter. This shape of 5 squares has perimeter 12 units.

5 squares → 12 units

Remember

• A diagonal cuts a rectangle into two equal triangles.
• Area of a triangle = ½ × base × height.
• Shapes with the same area can have different perimeters.

Quick check

A triangle has base 10 cm and height 6 cm. What is its area?

1. 16 sq cm
2. 30 sq cm
3. 60 sq cm
4. 32 cm

Think about it

Using 10 unit squares joined edge to edge, what is the smallest perimeter you can make? The largest?

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.